Current density functional framework for spin-orbit coupling.

Relativistic two-component density functional calculations are carried out in a non-collinear formalism to describe spin-orbit interactions, where the exchange-correlation functional is constructed as a generalization of the non-relativistic density functional approximation. Contrary to non-relativistic density functional theory (DFT), spin-orbit coupling, however, leads to a non-vanishing paramagnetic current density. Density functionals depending on the kinetic energy density, such as meta-generalized gradient approximations, should therefore be constructed in the framework of current DFT (CDFT). The latter has previously exclusively been used in the regime of strong magnetic fields. Herein, we present a consistent CDFT approach for relativistic DFT, including spin-orbit coupling. Furthermore, we assess the importance of the current density terms for ground-state energies, excitation energies, nuclear magnetic resonance shielding, and spin-spin coupling constants, as well as hyperfine coupling constants, Δg-shifts, and the nuclear quadrupole interaction tensor in electron paramagnetic resonance (EPR) spectroscopy. The most notable changes are found for EPR properties. The impact of the current-dependent terms rises with the number of unpaired electrons, and consequently, the EPR properties are more sensitive toward CDFT. Considerable changes are observed for the strongly constrained and appropriately normed functionals, as well as the B97M family and TASK. The current density terms are less important when exact exchange is incorporated. At the same time, the current-dependent kernel ensures the stability of response calculations in all cases. We, therefore, strongly recommend to use the framework of CDFT for self-consistent spin-orbit calculations.

Molecular dynamics of linear molecules in strong magnetic fields.

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born-Oppenheimer potential energy surfaces are calculated at the Hartree-Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.

Chiral Resolution of Spin-Crossover Active Iron(II) [2x2] Grid Complexes.

Chiral magnetic materials are proposed for applications in second-order non-linear optics, magneto-chiral dichroism, among others. Recently, we have reported a set of tetra-nuclear Fe(II) grid complex conformers with general formula C/S-[Fe4 L4 ]8+ (L: 2,6-bis(6-(pyrazol-1-yl)pyridin-2-yl)-1,5-dihydrobenzo[1,2-d : 4,5-d']diimidazole). In the grid complexes, isomerism emerges from tautomerism and conformational isomerism of the ligand L, and the S-type grid complex is chiral, which originates from different non-centrosymmetric spatial organization of the trans type ligand around the Fe(II) center. However, the selective preparation of an enantiomerically pure grid complex in a controlled manner is difficult due to spontaneous self-assembly. To achieve the pre-synthesis programmable resolution of Fe(II) grid complexes, we designed and synthesized two novel intrinsically chiral ligands by appending chiral moieties to the parent ligand. The complexation of these chiral ligands with Fe(II) salt resulted in the formation of enantiomerically pure Fe(II) grid complexes, as unambiguously elucidated by CD and XRD studies. The enantiomeric complexes exhibited similar gradual and half-complete thermal and photo-induced SCO characteristics. The good agreement between the experimentally obtained and calculated CD spectra further supports the enantiomeric purity of the complexes and even the magnetic studies. The chiral resolution of Fe(II)- [2×2] grid complexes reported in this study, for the first time, might enable the fabrication of magneto-chiral molecular devices.

Molecular point groups and symmetry in external magnetic fields.

As quantum-chemical calculations of molecules in static external magnetic fields are becoming increasingly popular, the description of molecular symmetry under such conditions is also becoming more and more relevant. Using group theory, a general scheme of identifying the molecular point group in an external magnetic field is constructed. For both point groups that are non-existent in the absence of a field (C∞ and C∞ h) and their double groups, the character tables are presented. General properties of all possible point groups are discussed, and it is mathematically proven that they are all Abelian.

Computation of Electromagnetic Properties of Molecular Ensembles.

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum-chemical simulations and the transfer matrix (T-matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time-dependent Hartree-Fock theory simulation data of a single chiral molecule to compute the T-matrix of a cross-like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum-mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T-matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T-matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T-matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T-matrix-based formulas for computing traditional chiro-optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light-matter interactions of arbitrarily-high multipolar orders.

Consistent Analytical Second Derivatives of the Kohn-Sham DFT Energy in the Framework of the Conductor-Like Screening Model through Gaussian Charge Distributions.

The use of implicit solvation models such as the conductor-like screening model (COSMO) in quantum chemical calculations is very common, as both a rough estimate of solvation effects as well as a general tool for stabilizing ionic molecular structures. In order to generate a smooth potential energy surface as well as consistent gradients, it is necessary to apply the Gaussian charge model (GCM) for the COSMO charges. This work introduces an efficient implementation for consistent analytical second derivatives of the electronic energy with COSMO-GCM in the framework of the Kohn-Sham density functional theory. This is used to investigate the infrared spectroscopy of amino acids in aqueous solution, where the impact of pH on the molecular structure and vibrational spectra is examined. Furthermore, the structure and stability of selected all-metal aromatic cluster ions are assessed.

TURBOMOLE: Today and Tomorrow.

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Linear Response of Current-Dependent Density Functional Approximations in Magnetic Fields.

This Letter outlines the steps and derivations that are necessary to apply density functional approximations that depend on the current and kinetic energy density rigorously within the framework of linear-response methods, including adiabatic time-dependent current density functional theory. This includes systems with a non-zero current density in the ground state. The necessary exchange-correlation kernel for these density functional approximations is derived, and the matrix elements are given explicitly. Due to the gauge variance of the kinetic energy density in an external magnetic field, having access to the proper current-dependent exchange-correlation kernel is necessary to recover gauge invariance for excited states. As a proof of principle application, the excited states of two small molecules in strong external magnetic fields are calculated using linear-response time-dependent current density functional theory. Finally, the implications of the derived current density-dependent exchange-correlation kernel for systems with strong spin-orbit coupling are discussed.

Efficient Calculation of Magnetic Circular Dichroism Spectra Using Spin-Noncollinear Linear-Response Time-Dependent Density Functional Theory in Finite Magnetic Fields.

Excited-state calculations in finite magnetic fields are presented in the framework of spin-noncollinear linear-response time-dependent density functional theory. To ensure gauge-origin invariance, London atomic orbitals are employed throughout. An efficient implementation into the Turbomole package, which also includes the resolution of the identity approximation, allows for the investigation of excited states of large molecular systems. The implementation is used to investigate the magnetic circular dichroism spectra of sizable organometallic molecules such as a zinc tetraazaporphyrin with two fused naphthalene units, which is a molecule with 57 atoms.

The GW/BSE Method in Magnetic Fields.

The GW approximation and the Bethe-Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.